Consider the following scenario:

Five pirates wish to divide the loot of a 100 gold pieces. They are democratic pirates, in their own way, and it is their custom to make such divisions in the following manner: The fiercest pirate makes a proposal about the division and everybody (including the proposer) votes on it. If 50 percent or more are in favor, the proposal is implemented. Otherwise the proposer is thrown overboard, and the procedure is repeated with the next fiercest pirate.

All the pirates enjoy throwing their fellows overboard, but given a choice they prefer more gold. Of course, they intensely dislike being thrown overboard themselves. (Specifically, we say that each pirate assigns a utility of 1 to each gold piece, a utility of 1/100 to throwing another pirate overboard, and a utility of −1000 to being thrown overboard). All pirates are rational and know that the other pirates are also rational. Moreover, no two pirates are equally fierce, so there is a precise order, known to all, of making proposals. The gold pieces are indivisible and arrangements to share pieces are not permitted, because no pirate trusts his mates.

What proposal should the fiercest pirate make?